Atlas of Lie Groups Software Package: Helper Applications
These are various applications intended to be used in conjunction with
the Atlas software.
These are undergoing a constant state of development, and are not as
stable as the atlas software itself. Many of these features will
eventually be incorporated directly into the atlas software itself.
- Squashblock, by John
Stembridge.
- Produces snazzy pictures of posets obtained
from cells. See the README file.
- coherentContinuation (Right click to download
perl script coherentContinuation ).
(Works with atlas ouput 0.4*)
- Compute the coherent continuation action, using atlas output.
There are 3 versions:
- on a block in terms of the basis of standard modules (output of the block command)
- on a block in terms of the basis of irreducible modules (output of the wgraph command)
- on a list of cells, in terms of the basis of irreducible modules
(output of the wcells command)
Output is in mathematica or maple format.
kl (Right click to download perl script kl ).
(Works with atlas ouput 0.4*)
Compute the Kazhdan-Lusztig matrix for a block, using
the output of the klbasis command of atlas.
Output is in mathematica or maple format.
q=1 (Right click to download perl script
q=1 ) (works with atlas version 0.4*)
Set q=1 in the Kazhdan-Lusztig polynomials. For example here is
the beginning of the list of
the polynmials for the large block of E7 with q set equal to 1. The largest number
appearing is 13,620.
blockj (Right click to download perl script blockj ) (works with atlas version 0.4*)
Takes the output of the block command of atlas,
and adds some information to it: real Cayley transforms, and also
gives the sequences of Cayley transforms and cross actions taking a
fundamental series to each parameter. Alternatively gives the sequences taking a
single fundamental series to each parameter (and similarly starting on
the most split Cartan).
Here is a C3 example.
isomorphisms of blocks (Right click to downloaod
perl script isos.pl)
(Works with atlas version 0.4*)
Computes isomorphisms of two blocks given by output of
block command. By Hunter Brooks at Maryland,
nnn9245@gmail.com. Not well documented, but pretty self-explanatory.
Computes all isomorphisms obtained by varying starting points in the
parametrization of blocks by "pairs of chains" [Vogan, Irreducible
Characters 4, Duke #49, 1992]. Also optionally allows permutations of
simple roots. Might give all isomorphisms? Alternative version:
bigisos.pl, which works on bigger blocks
like E8, at a cost of speed but savings of memory.
Here are some examples.
Originally written for 0.3 output.
testAtlas (Right click to download perl script testAtlas.pl.)
(Works with atlas ouput 0.4*)
This perl script is used for producing the tables in tables/atlas, and for testing the atlas
software.
It does several things:
(1) create directory tree and an input file to atlas
(2) runs atlas to populate the tree with data files
(3) computes checksums on these files
(4) compares checksums with a
checksums reference file.
Download the perl script, make it executable, and give the command
./testAtlas.pl -h for more information, or see the
README file.
Note: The format of the output files has changed in
version 0.3. Therefore the checksums reference file should
only be used for testing version 0.3 and later. For the record here is
the version of the
checksum file for
version 0.2 and earlier.
Parameters: Program to take output of the block
command and give human readable parameters for classical groups.
(Works with atlas ouput 0.4*)
Download parameters.tgz or right click
to download just the perl script parameters.
The script and many examples are in the parameters directory,
and here are the slides from my talk
at the AMS meeting in Kalamazoo, October 2008 (corrected 10/21/08).
Stable Characters (Right click to download perl
script: stable.) Warning: currently poorly documented and
not user friendly. Here are some examples.
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